document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1124204>Question 1124204</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jack used 54 ft of forming and 24 cubic ft of concrete to pour a sidewalk 4 inches thick.  Assuming that the length is the larger of the dimensions, what was the length of the sidewalk? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #740558 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=740558\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the 54 feet of framing formed the perimeter of the sidewalk.<BR>\n" );
document.write( "let L equal the length and W equal the width to get 2L + 2W = 54<BR>\n" );
document.write( "divide both sides of this equation by 2 to get L + W = 27.\r<BR>\n" );
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document.write( "the volume of the sidewalk is equal to 24 cubic feet.<BR>\n" );
document.write( "that would be L * W * D = 24<BR>\n" );
document.write( "D is the depth, which is 4 inches which is 1/3 feet deep.<BR>\n" );
document.write( "therefore L * W * D = 24 becomes L * W * 1/3 = 24<BR>\n" );
document.write( "multiply both sides of this equation by 3/2 to get L * W = 72\r<BR>\n" );
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document.write( "you have 2 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are L + W = 27 and L * W = 72\r<BR>\n" );
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document.write( "solve for L in both equations to get L = 27 - W and L = 72/W\r<BR>\n" );
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document.write( "since they're both equal to L, then 27 - W = 72 / W\r<BR>\n" );
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document.write( "multiply both sides of this equation by W to get 27W - W^2 = 72\r<BR>\n" );
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document.write( "subtract 27W from both sides of this equation and add W^2 to both sides of this equation and order the terms by descending order of degree to get:\r<BR>\n" );
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document.write( "0 = W^2 - 27W + 72 which is the same as W^2 - 27W + 72 = 0\r<BR>\n" );
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document.write( "factor this quadratic equation to get (W - 3) * (W - 24) = 0<BR>\n" );
document.write( "solve for W to get W = 3 or W = 24.\r<BR>\n" );
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document.write( "since W is the smaller dimension, then W = 3.<BR>\n" );
document.write( "since L + W = 27, then L must be equal to 24 because 3 + 24 = 27.\r<BR>\n" );
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document.write( "you have L = 24 and W = 3\r<BR>\n" );
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document.write( "L + W = 24 + 3 = 27<BR>\n" );
document.write( "L * W = 24 * 3 = 72<BR>\n" );
document.write( "L * W * D = 24 * 3 * 1/3 = 24\r<BR>\n" );
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document.write( "the solution looks good.<BR>\n" );
document.write( "the solution is that the length of the sidewalk is 24 feet.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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